One oscillation that Pearson investigated was that of transverse waves induced by climbers. The bottom line on this oscillation is that large oscillations can be induced when the climber transverses the length of the cable in one period of the cable's characteristic frequency. (Pearson assumed no counterweight so had the climber traveling twice the length of the cable during one period.) Since we just calculated our cable's characteristic period to be 7.1 hours we will only need to worry about this particular affect when we plan to have climbers traveling at close to 10,000 km/hr.
A little more googling pulls up a set of presentation slides demonstrating (I think) how oscillations from "climber" loads would be damped by modulation of "tension".
I just had another discussion with an officemate who is dubious of the idea of a 120,000 km object being in "geosynchronous orbit", and says that you can't have a gravitational force diagram, treated as a single point, of something that extends over planetary scales. Eh, I figure that if it works for planets, why not something much smaller, if considerably longer?
I don't claim to understand this stuff, or that any of the above is right. I'm just wondering if there isn't a certain class of problem in which you can know just enough to make a fool of yourself in. If there is, Den Beste is definitely a specialist in that field. Me? I'm just an idiot with a Google taskbar.